The rise or an increase in altitude is represented by positive sign and a decend or decrease in altitude is represented by negative sign.
First the helicopter descended 1200 feet. So the change in altitude will be -1200 feet.
Then the helicopter rose by 800 feet. So the change in altitude will be 800 feet.
Finally the helicopter descended by 450 feet. So the change in altitude will be -450 feet.
The net change in altitude will be the sum of all the above 3 changes.
Change in altitude = -1200 + 800 - 450 = -850 feet
The negative sign indicates a descend i.e. loss in altitude. So the net change in altitude was a loss of 850 feet.
if we zero out f(x), namely make y = 0, we can get the roots or x-intercepts for this quadratic equation
![\bf 0 = (x+4)(x-2)\implies \begin{cases} 0=x+4\implies &-4=x\\ 0=x-2\implies &2=x \end{cases}](https://tex.z-dn.net/?f=%5Cbf%200%20%3D%20%28x%2B4%29%28x-2%29%5Cimplies%20%5Cbegin%7Bcases%7D%200%3Dx%2B4%5Cimplies%20%26-4%3Dx%5C%5C%200%3Dx-2%5Cimplies%20%262%3Dx%20%5Cend%7Bcases%7D)
now, the equation is in x-terms, meaning is a vertically opening parabola, so the axis of symmetry will be x = something, a vertical line.
well, we have two x-intercepts, one at -4 and another at 2, and the vertex is right half-way between those guys
-4------------(-1)------------2
so the vertex is at x=-1, namely the axis of symmetry is x = -1.
Answer:
![\sf -11+7\sqrt{2}](https://tex.z-dn.net/?f=%5Csf%20-11%2B7%5Csqrt%7B2%7D)
Step-by-step explanation:
Given expression:
![\sf \dfrac{3-\sqrt{32}}{1+\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B3-%5Csqrt%7B32%7D%7D%7B1%2B%5Csqrt%7B2%7D%20%7D)
Rewrite 32 as 16 · 2:
![\sf \implies \dfrac{3-\sqrt{16 \cdot 2}}{1+\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-%5Csqrt%7B16%20%5Ccdot%202%7D%7D%7B1%2B%5Csqrt%7B2%7D%20%7D)
Apply radical rule ![\sf \sqrt{a \cdot b}=\sqrt{a}\sqrt{b}](https://tex.z-dn.net/?f=%5Csf%20%5Csqrt%7Ba%20%5Ccdot%20b%7D%3D%5Csqrt%7Ba%7D%5Csqrt%7Bb%7D)
![\sf \implies \dfrac{3-\sqrt{16}\sqrt{2}}{1+\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-%5Csqrt%7B16%7D%5Csqrt%7B2%7D%7D%7B1%2B%5Csqrt%7B2%7D%20%7D)
As
:
![\sf \implies \dfrac{3-4\sqrt{2}}{1+\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-4%5Csqrt%7B2%7D%7D%7B1%2B%5Csqrt%7B2%7D%20%7D)
Multiply by the conjugate:
![\sf \implies \dfrac{3-4\sqrt{2}}{1+\sqrt{2} } \times \dfrac{1-\sqrt{2} }{1-\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-4%5Csqrt%7B2%7D%7D%7B1%2B%5Csqrt%7B2%7D%20%7D%20%5Ctimes%20%5Cdfrac%7B1-%5Csqrt%7B2%7D%20%7D%7B1-%5Csqrt%7B2%7D%20%7D)
![\sf \implies \dfrac{(3-4\sqrt{2})(1-\sqrt{2})}{(1+\sqrt{2})(1-\sqrt{2})}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B%283-4%5Csqrt%7B2%7D%29%281-%5Csqrt%7B2%7D%29%7D%7B%281%2B%5Csqrt%7B2%7D%29%281-%5Csqrt%7B2%7D%29%7D)
![\sf \implies \dfrac{3-3\sqrt{2}-4\sqrt{2}+4\sqrt{2}\sqrt{2}}{1-\sqrt{2}+\sqrt{2}-\sqrt{2}\sqrt{2}}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-3%5Csqrt%7B2%7D-4%5Csqrt%7B2%7D%2B4%5Csqrt%7B2%7D%5Csqrt%7B2%7D%7D%7B1-%5Csqrt%7B2%7D%2B%5Csqrt%7B2%7D-%5Csqrt%7B2%7D%5Csqrt%7B2%7D%7D)
As
:
![\sf \implies \dfrac{3-3\sqrt{2}-4\sqrt{2}+4 \cdot 2}{1-\sqrt{2}+\sqrt{2}-2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-3%5Csqrt%7B2%7D-4%5Csqrt%7B2%7D%2B4%20%5Ccdot%202%7D%7B1-%5Csqrt%7B2%7D%2B%5Csqrt%7B2%7D-2%7D)
![\sf \implies \dfrac{3-7\sqrt{2}+8}{1-2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B3-7%5Csqrt%7B2%7D%2B8%7D%7B1-2%7D)
![\sf \implies \dfrac{11-7\sqrt{2}}{-1}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B11-7%5Csqrt%7B2%7D%7D%7B-1%7D)
![\sf \implies -11+7\sqrt{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20-11%2B7%5Csqrt%7B2%7D)
Answer:288pi
Step-by-step explanation:4/3pir^3 6^3*4/3*pi 216*4/3*pi 288pi